Quantum mechanics famously posits two distinct evolution rules for the state of a system: a
deterministic, unitary time evolution under the Schr¨odinger equation, and a probabilistic “collapse”
of the wavefunction upon measurement as dictated by the Born rule. The apparent inconsistency
of these two dynamical laws – one continuous and one discontinuous – constitutes the quantum
measurement problem. This foundational problem, which underlies the emergence of definite outcomes
from quantum superpositions, has persisted since the theory’s inception. In this review, we
present a comprehensive and rigorous examination of the measurement problem and survey the
leading approaches that seek to resolve or circumvent it. We begin by formulating the measurement
problem and its conceptual challenges. We then discuss in detail the major interpretations of quantum
mechanics and theoretical frameworks addressing the problem: the Copenhagen interpretation,
Everett’s many-worlds interpretation, de Broglie–Bohm pilot-wave theory, objective collapse models,
the role of decoherence and environment-induced superselection, and epistemic approaches such
as QBism. For each interpretation, we describe the core principles and mathematical formalism,
assessing how (and whether) it attempts to solve the measurement problem. We also review modern
developments and experiments relevant to quantum measurements, including tests of Bell inequalities,
observations of decoherence and macroscopic superpositions, weak measurements and quantum
eraser experiments, and thought experiments ‘a la Wigner’s friend. We highlight how these results
inform the ongoing debate. Finally, we discuss open problems and challenges that remain in fully
resolving the measurement problem.